Integers

Definition

Integers are a set of positive and negative whole numbers, including zero. They are the foundation for many mathematical operations and concepts, and are essential in understanding and working with various topics in pre-algebra.

5 Must Know Facts For Your Next Test

1. Integers can be used to represent quantities, such as the number of items in a collection or the temperature above or below a reference point.
2. The four basic arithmetic operations (addition, subtraction, multiplication, and division) can be performed on integers, with the results also being integers.
3. Integers are used to find multiples and factors of numbers, which is important in understanding number patterns and relationships.
4. Solving equations with integers involves applying the properties of equality, including the division property, to find unknown values.
5. Integers are a subset of rational numbers, which also include fractions and can be used to represent more complex mathematical concepts.

Review Questions

• Explain how integers are used in the context of subtracting whole numbers.
  • Integers are essential in the process of subtracting whole numbers. When subtracting a larger whole number from a smaller whole number, the result is a negative integer. For example, subtracting 7 from 3 results in the negative integer -4. Integers allow us to represent and work with these negative values, which is crucial for understanding the relationship between whole numbers and the differences between them.
• Describe how integers are used in the context of multiplying whole numbers.
  • Integers play a key role in the multiplication of whole numbers. The product of two positive whole numbers is a positive integer, while the product of a positive and a negative whole number is a negative integer. Additionally, the product of two negative whole numbers is also a positive integer. Understanding these patterns and properties of integer multiplication is essential for working with whole numbers and developing fluency in pre-algebra concepts.
• Analyze how the concept of integers is used to find multiples and factors of numbers.
  • Integers are fundamental in the process of finding multiples and factors of numbers. Multiples of a number are the products of that number and other integers, both positive and negative. Factors of a number are the integers that divide the number evenly. Identifying multiples and factors is crucial for recognizing number patterns, simplifying expressions, and solving equations involving integers in pre-algebra.

Related terms

Whole Numbers: Whole numbers are a subset of integers, consisting of the non-negative integers (0, 1, 2, 3, and so on).

Absolute Value: The absolute value of an integer is the distance of that integer from zero on the number line, regardless of its sign.

Number Line: A number line is a visual representation of the set of integers, with positive integers to the right of zero and negative integers to the left.